SOLVE ONLY PARTS I) AND II), USING ONLY FORMULAS, NO TABLES, CORRECT ANSWERS ARE FOR I) A(T) = EXP(0.03T+ 0.0025T^2) FOR 0 6 (i) (ii) Derive, and simplify as far as possible, expressions in terms of t for the accumulated amount at time t of an investment of £1 made at time t = 0. You should derive separate expressions for both sub-intervals. Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000 made at time t = 7. (iii) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). (iv) A continuous payment stream, under which the rate of payment per annum at time t is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in part (i), calculate the present value (at time t = 0) of this investment.
SOLVE ONLY PARTS I) AND II), USING ONLY FORMULAS, NO TABLES, CORRECT ANSWERS ARE FOR I) A(T) = EXP(0.03T+ 0.0025T^2) FOR 0 6 (i) (ii) Derive, and simplify as far as possible, expressions in terms of t for the accumulated amount at time t of an investment of £1 made at time t = 0. You should derive separate expressions for both sub-intervals. Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000 made at time t = 7. (iii) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest convertible half-yearly implied by the transaction in part (ii). (iv) A continuous payment stream, under which the rate of payment per annum at time t is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in part (i), calculate the present value (at time t = 0) of this investment.
Chapter4: Time Value Of Money
Section4.12: Uneven, Or Irregular, Cash Flows
Problem 1ST
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PLEASE, WRITE THE SOLUTIONS ON PAPER, EXPLAINING THE ENTIRE PROCESS, THE ONLY POSSIBLE SOLUTIONS ARE THE STIPULATED ONES
Transcribed Image Text:SOLVE ONLY PARTS I) AND II), USING ONLY FORMULAS, NO TABLES, CORRECT ANSWERS ARE FOR I) A(T) = EXP(0.03T+
0.0025T^2) FOR 0 <T<6 AND A(T) = EXP(-0.09 + 0.06T) FOR 6 < T. AND FOR II) C3 = £2000 X (EXP(0.1125)) / (EXP(0.33)) =
£1,609.05
The force of interest 8 (t) is a function of time and at any time t, measured in years, is given
by the formula:
8(t)
={0.03
(0.03+0.005t
0.06
for
0<t≤ 6
for
t> 6
(i)
(ii)
Derive, and simplify as far as possible, expressions in terms of t for the
accumulated amount at time t of an investment of £1 made at time t = 0. You
should derive separate expressions for both sub-intervals.
Using the result in part (i), calculate the value at time t = 3 of a payment of £2,000
made at time t = 7.
(iii) Calculate, to the nearest 0.1%, the constant nominal annual rate of interest
convertible half-yearly implied by the transaction in part (ii).
(iv) A continuous payment stream, under which the rate of payment per annum at time t
is p(t) = 500e-0.01t, is invested between t = 10 and t = 15. Using the result in
part (i), calculate the present value (at time t = 0) of this investment.
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